Admit your guilt. If the teacher caught you cheating, he actually saw you in the act. There is no need to lie about it or try to get out of the situation.
Explain why you were cheating. There has to be a reason behind your temptation to cheat. Tell the teacher the truth. If you are lucky, your teacher will accept your explanation.
Offer to do the assignment or test over again before or after school. Apologize for cheating the first time, and then offer to redo the assignment. If the teacher does not allow you to redo the assignment, accept your zero as a punishment.
Remain calm. You knew that you were doing wrong and it would not be right to fight with your teacher when you know you are in the wrong.
Tell you teacher that it will not happen again. It is important that you learn your lesson. Next time, your teacher may not be as nice.